Key Terms, Key Equations, Summaries, and Exercises (Chapter 3)

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Key Terms, Key Equations, Summaries, and Exercises (Chapter 3)

Key Terms

actinide: inner transition metal in the bottom of the bottom two rows of the periodic table

alkali metal: element in group 1

alkaline earth metal: element in group 2

amplitude: extent of the displacement caused by a wave

atomic orbital: mathematical function that describes the behavior of an electron in an atom (also called the wavefunction)

Aufbau principle: procedure in which the electron configuration of the elements is determined by “building” them in order of atomic numbers, adding one proton to the nucleus and one electron to the proper subshell at a time

blackbody: idealized perfect absorber of all incident electromagnetic radiation; such bodies emit electromagnetic radiation in characteristic continuous spectra called blackbody radiation

Bohr’s model of the hydrogen atom: structural model in which an electron moves around the nucleus only in circular orbits, each with a specific allowed radius

chalcogen: element in group 16

continuous spectrum: electromagnetic radiation given off in an unbroken series of wavelengths (e.g., white light from the sun)

core electron: electron in an atom that occupies the orbitals of the inner shells

covalent bond: attractive force between the nuclei of a molecule’s atoms and pairs of electrons between the atoms

covalent compound: (also, molecular compound) composed of molecules formed by atoms of two or more different elements

covalent radius: one-half the distance between the nuclei of two identical atoms when they are joined by a covalent bond

d orbital: region of space with high electron density that is either four lobed or contains a dumbbell and torus shape; describes orbitals with l = 2.

degenerate orbitals: orbitals that have the same energy

effective nuclear charge: charge that leads to the Coulomb force exerted by the nucleus on an electron, calculated as the nuclear charge minus shielding

electromagnetic radiation: energy transmitted by waves that have an electric-field component and a magnetic-field component

electromagnetic spectrum: range of energies that electromagnetic radiation can comprise, including radio, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays

electron affinity: energy change associated with addition of an electron to a gaseous atom or ion

electron configuration: listing that identifies the electron occupancy of an atom’s shells and subshells

electron density: a measure of the probability of locating an electron in a particular region of space, it is equal to the squared absolute value of the wave function ψ

endothermic: processes that increase the energy of an atom and involve the absorption of light

excited state: state having an energy greater than the ground-state energy

exothermic: processes that decrease the energy of an atom and involve the emission of light

f orbital: multilobed region of space with high electron density, describes orbitals with l = 3

frequency (ν): number of wave cycles (peaks or troughs) that pass a specified point in space per unit time

ground state: state in which the electrons in an atom, ion, or molecule have the lowest energy possible

group: vertical column of the periodic table

halogen: element in group 17

Heisenberg uncertainty principle: rule stating that it is impossible to exactly determine both certain conjugate dynamical properties such as the momentum and the position of a particle at the same time. The uncertainty principle is a consequence of quantum particles exhibiting wave–particle duality

hertz (Hz): the unit of frequency, which is the number of cycles per second, s⁻¹

Hund’s rule: every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin

inert gas: (also, noble gas) element in group 18

inner transition metal: (also, lanthanide or actinide) element in the bottom two rows; if in the first row, also called lanthanide, or if in the second row, also called actinide

intensity: property of wave-propagated energy related to the amplitude of the wave, such as brightness of light or loudness of sound

interference pattern: pattern typically consisting of alternating bright and dark fringes; it results from constructive and destructive interference of waves

ionic bond: electrostatic forces of attraction between the oppositely charged ions of an ionic compound

ionic compound: compound composed of cations and anions combined in ratios, yielding an electrically neutral substance

ionization energy: energy required to remove an electron from a gaseous atom or ion

isoelectronic: group of ions or atoms that have identical electron configurations

lanthanide: inner transition metal in the top of the bottom two rows of the periodic table

line spectrum: electromagnetic radiation emitted at discrete wavelengths by a specific atom (or atoms) in an excited state

magnetic quantum number (m_l): quantum number signifying the orientation of an atomic orbital around the nucleus

main-group element: (also, representative element) element in groups 1, 2, and 13–18

metal: element that is shiny, malleable, good conductor of heat and electricity

metalloid: element that conducts heat and electricity moderately well, and possesses some properties of metals and some properties of nonmetals

molecular compound: (also, covalent compound) composed of molecules formed by atoms of two or more different elements

monatomic ion: ion composed of a single atom

noble gas: (also, inert gas) element in group 18

node: any point of a standing wave with zero amplitude

nonmetal: element that appears dull, poor conductor of heat and electricity

orbital diagram: pictorial representation of the electron configuration showing each orbital as a box and each electron as an arrow

oxyanion: polyatomic anion composed of a central atom bonded to oxygen atoms

p orbital: dumbbell-shaped region of space with high electron density, describes orbitals with l = 1

Pauli exclusion principle: specifies that no two electrons in an atom can have the same value for all four quantum numbers

period: (also, series) horizontal row of the periodic table

periodic law: properties of the elements are periodic function of their atomic numbers

periodic table: table of the elements that places elements with similar chemical properties close together

photon: smallest possible packet of electromagnetic radiation, a particle of light

pnictogen: element in group 15

polyatomic ion: ion composed of more than one atom

principal quantum number (n): quantum number specifying the shell an electron occupies in an atom

quantization: limitation of some property to specific discrete values, not continuous

quantum mechanics: field of study that includes quantization of energy, wave-particle duality, and the Heisenberg uncertainty principle to describe matter

quantum number: number having only specific allowed values and used to characterize the arrangement of electrons in an atom

representative element: (also, main-group element) element in columns 1, 2, and 12–18

s orbital: spherical region of space with high electron density, describes orbitals with l = 0

secondary (angular momentum) quantum number (l): quantum number distinguishing the different shapes of orbitals; it is also a measure of the orbital angular momentum

series: (also, period) horizontal row of the period table

shell: atomic orbitals with the same principal quantum number, n

spin quantum number (m_s)

number specifying the electron spin direction, either

+ \frac{1}{2}

or $- \frac{1}{2}$

standing wave: (also, stationary wave) localized wave phenomenon characterized by discrete wavelengths determined by the boundary conditions used to generate the waves; standing waves are inherently quantized

subshell: atomic orbitals with the same values of n and l

transition metal: element in groups 3–12 (more strictly defined, 3–11; see chapter on transition metals and coordination chemistry)

valence electrons: electrons in the outermost or valence shell (highest value of n) of a ground-state atom

valence shell: outermost shell of electrons in a ground-state atom

wave: oscillation of a property over time or space; can transport energy from one point to another

wave-particle duality: observation that elementary particles can exhibit both wave-like and particle-like properties

wavefunction (ψ): mathematical description of an atomic orbital that describes the shape of the orbital; it can be used to calculate the probability of finding the electron at any given location in the orbital, as well as dynamical variables such as the energy and the angular momentum

wavelength (λ): distance between two consecutive peaks or troughs in a wave

Key Equations

c = λν

E = h ν = \frac{h c}{λ},

where h = 6.626 $\times$

10⁻³⁴ J s

\frac{1}{λ} = R_{\infty} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

E_{n} = - \frac{k Z^{2}}{n^{2}}, n = 1, 2, 3, \dots

Δ E = k Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

r = \frac{n^{2}}{Z} a_{0}

Summaries

3.1Electromagnetic Energy

Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, c, of 2.998 $\times$ 10⁸ m s⁻¹. This radiation shows wavelike behavior, which can be characterized by a frequency, ν, and a wavelength, λ, such that c = λν. Light is an example of a travelling wave. Other important wave phenomena include standing waves, periodic oscillations, and vibrations. Standing waves exhibit quantization, since their wavelengths are limited to discrete integer multiples of some characteristic lengths. Electromagnetic radiation that passes through two closely spaced narrow slits having dimensions roughly similar to the wavelength will show an interference pattern that is a result of constructive and destructive interference of the waves. Electromagnetic radiation also demonstrates properties of particles called photons. The energy of a photon is related to the frequency (or alternatively, the wavelength) of the radiation as E = hν (or $E = \frac{h c}{λ}$ ), where h is Planck’s constant. That light demonstrates both wavelike and particle-like behavior is known as wave-particle duality. All forms of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves interact differently with matter and have very different practical applications. Electromagnetic radiation can be generated by exciting matter to higher energies, such as by heating it. The emitted light can be either continuous (incandescent sources like the sun) or discrete (from specific types of excited atoms). Continuous spectra often have distributions that can be approximated as blackbody radiation at some appropriate temperature. The line spectrum of hydrogen can be obtained by passing the light from an electrified tube of hydrogen gas through a prism. This line spectrum was simple enough that an empirical formula called the Rydberg formula could be derived from the spectrum. Three historically important paradoxes from the late 19th and early 20th centuries that could not be explained within the existing framework of classical mechanics and classical electromagnetism were the blackbody problem, the photoelectric effect, and the discrete spectra of atoms. The resolution of these paradoxes ultimately led to quantum theories that superseded the classical theories.

3.2The Bohr Model

Bohr incorporated Planck’s and Einstein’s quantization ideas into a model of the hydrogen atom that resolved the paradox of atom stability and discrete spectra. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon. To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.

3.3Development of Quantum Theory

Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. Their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. Atomic wavefunctions are also called orbitals. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in space. Therefore, atomic orbitals describe the areas in an atom where electrons are most likely to be found.

An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, can be any positive integer. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n. Orbitals having the same value of n are said to be in the same shell. The secondary (angular momentum) quantum number, l, can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principal quantum number and the same l value belong to the same subshell. The magnetic quantum number, m_l, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. In addition, each electron has a spin quantum number, m_s, that can be equal to $\pm \frac{1}{2} .$ No two electrons in the same atom can have the same set of values for all the four quantum numbers.

3.4Electronic Structure of Atoms (Electron Configurations)

The relative energy of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on). Electron configurations and orbital diagrams can be determined by applying the Pauli exclusion principle (no two electrons can have the same set of four quantum numbers) and Hund’s rule (whenever possible, electrons retain unpaired spins in degenerate orbitals).

Electrons in the outermost orbitals, called valence electrons, are responsible for most of the chemical behavior of elements. In the periodic table, elements with analogous valence electron configurations usually occur within the same group. There are some exceptions to the predicted filling order, particularly when half-filled or completely filled orbitals can be formed. The periodic table can be divided into three categories based on the orbital in which the last electron to be added is placed: main group elements (s and p orbitals), transition elements (d orbitals), and inner transition elements (f orbitals).

3.5Periodic Variations in Element Properties

Electron configurations allow us to understand many periodic trends. Covalent radius increases as we move down a group because the n level (orbital size) increases. Covalent radius mostly decreases as we move left to right across a period because the effective nuclear charge experienced by the electrons increases, and the electrons are pulled in tighter to the nucleus. Anionic radii are larger than the parent atom, while cationic radii are smaller, because the number of valence electrons has changed while the nuclear charge has remained constant. Ionization energy (the energy associated with forming a cation) decreases down a group and mostly increases across a period because it is easier to remove an electron from a larger, higher energy orbital. Electron affinity (the energy associated with forming an anion) is more favorable (exothermic) when electrons are placed into lower energy orbitals, closer to the nucleus. Therefore, electron affinity becomes increasingly negative as we move left to right across the periodic table and decreases as we move down a group. For both IE and electron affinity data, there are exceptions to the trends when dealing with completely filled or half-filled subshells.

3.6The Periodic Table

The discovery of the periodic recurrence of similar properties among the elements led to the formulation of the periodic table, in which the elements are arranged in order of increasing atomic number in rows known as periods and columns known as groups. Elements in the same group of the periodic table have similar chemical properties. Elements can be classified as metals, metalloids, and nonmetals, or as a main-group elements, transition metals, and inner transition metals. Groups are numbered 1–18 from left to right. The elements in group 1 are known as the alkali metals; those in group 2 are the alkaline earth metals; those in 15 are the pnictogens; those in 16 are the chalcogens; those in 17 are the halogens; and those in 18 are the noble gases.

3.7Molecular and Ionic Compounds

Metals (particularly those in groups 1 and 2) tend to lose the number of electrons that would leave them with the same number of electrons as in the preceding noble gas in the periodic table. By this means, a positively charged ion is formed. Similarly, nonmetals (especially those in groups 16 and 17, and, to a lesser extent, those in Group 15) can gain the number of electrons needed to provide atoms with the same number of electrons as in the next noble gas in the periodic table. Thus, nonmetals tend to form negative ions. Positively charged ions are called cations, and negatively charged ions are called anions. Ions can be either monatomic (containing only one atom) or polyatomic (containing more than one atom).

Compounds that contain ions are called ionic compounds. Ionic compounds generally form from metals and nonmetals. Compounds that do not contain ions, but instead consist of atoms bonded tightly together in molecules (uncharged groups of atoms that behave as a single unit), are called covalent compounds. Covalent compounds usually form from two nonmetals.

Exercises

3.1 Electromagnetic Energy

1.

The light produced by a red neon sign is due to the emission of light by excited neon atoms. Qualitatively describe the spectrum produced by passing light from a neon lamp through a prism.

2.

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 $\times$ 10⁸ s⁻¹ (103.1 MHz). What is the wavelength of these radio waves in meters?

3.

FM-95, an FM radio station, broadcasts at a frequency of 9.51 $\times$ 10⁷ s⁻¹ (95.1 MHz). What is the wavelength of these radio waves in meters?

4.

A bright violet line occurs at 435.8 nm in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light?

5.

Light with a wavelength of 614.5 nm looks orange. What is the energy, in joules, per photon of this orange light? What is the energy in eV (1 eV = 1.602 $\times$ 10⁻¹⁹ J)?

6.

Heated lithium atoms emit photons of light with an energy of 2.961 $\times$ 10⁻¹⁹ J. Calculate the frequency and wavelength of one of these photons. What is the total energy in 1 mole of these photons? What is the color of the emitted light?

7.

A photon of light produced by a surgical laser has an energy of 3.027 $\times$ 10⁻¹⁹ J. Calculate the frequency and wavelength of the photon. What is the total energy in 1 mole of photons? What is the color of the emitted light?

8.

When rubidium ions are heated to a high temperature, two lines are observed in its line spectrum at wavelengths (a) 7.9 $\times$ 10⁻⁷ m and (b) 4.2 $\times$ 10⁻⁷ m. What are the frequencies of the two lines? What color do we see when we heat a rubidium compound?

9.

The emission spectrum of cesium contains two lines whose frequencies are (a) 3.45 $\times$ 10¹⁴ Hz and (b) 6.53 $\times$ 10¹⁴ Hz. What are the wavelengths and energies per photon of the two lines? What color are the lines?

10.

Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of 1.5 $\times$ 10⁻⁶ m must be absorbed by the water to warm a cup of water (175 g) from 25.0 °C to 40 °C?

11.

One of the radiographic devices used in a dentist’s office emits an X-ray of wavelength 2.090 $\times$ 10⁻¹¹ m. What is the energy, in joules, and frequency of this X-ray?

12.

The eyes of certain reptiles pass a single visual signal to the brain when the visual receptors are struck by photons of a wavelength of 850 nm. If a total energy of 3.15 $\times$ 10⁻¹⁴ J is required to trip the signal, what is the minimum number of photons that must strike the receptor?

13.

RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?

14.

Answer the following questions about a Blu-ray laser:

(a) The laser on a Blu-ray player has a wavelength of 405 nm. In what region of the electromagnetic spectrum is this radiation? What is its frequency?

(b) A Blu-ray laser has a power of 5 milliwatts (1 watt = 1 J s⁻¹). How many photons of light are produced by the laser in 1 hour?

(c) The ideal resolution of a player using a laser (such as a Blu-ray player), which determines how close together data can be stored on a compact disk, is determined using the following formula: Resolution = 0.60(λ/NA), where λ is the wavelength of the laser and NA is the numerical aperture. Numerical aperture is a measure of the size of the spot of light on the disk; the larger the NA, the smaller the spot. In a typical Blu-ray system, NA = 0.95. If the 405-nm laser is used in a Blu-ray player, what is the closest that information can be stored on a Blu-ray disk?

(d) The data density of a Blu-ray disk using a 405-nm laser is 1.5 $\times$ 10⁷ bits mm⁻². Disks have an outside diameter of 120 mm and a hole of 15-mm diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold 9,400,000 pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by A = πr², where the radius r is one-half of the diameter.)

15.

What is the threshold frequency for sodium metal if a photon with frequency 6.66 $\times$ 10¹⁴ s⁻¹ ejects an electron with 7.74 $\times$ 10⁻²⁰ J kinetic energy? Will the photoelectric effect be observed if sodium is exposed to orange light?

3.2 The Bohr Model

16.

Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?

17.

What does it mean to say that the energy of the electrons in an atom is quantized?

18.

Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom. Show your calculations.

19.

The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV = 1.602 $\times$ 10^–19 J. Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with n = 2. Show your calculations.

20.

Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the Li²⁺ ion.

21.

Using the Bohr model, determine the lowest possible energy for the electron in the He⁺ ion.

22.

Using the Bohr model, determine the energy of an electron with n = 6 in a hydrogen atom.

23.

Using the Bohr model, determine the energy of an electron with n = 8 in a hydrogen atom.

24.

How far from the nucleus in angstroms (1 angstrom = 1 $\times$ 10^–10 m) is the electron in a hydrogen atom if it has an energy of –8.72 $\times$ 10^–20 J?

25.

What is the radius, in angstroms, of the orbital of an electron with n = 8 in a hydrogen atom?

26.

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a He⁺ ion moves from the orbit with n = 5 to the orbit with n = 2.

27.

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a Li²⁺ ion moves from the orbit with n = 2 to the orbit with n = 1.

28.

Consider a large number of hydrogen atoms with electrons randomly distributed in the n = 1, 2, 3, and 4 orbits.

(a) How many different wavelengths of light are emitted by these atoms as the electrons fall into lower-energy orbitals?

(b) Calculate the lowest and highest energies of light produced by the transitions described in part (a).

(c) Calculate the frequencies and wavelengths of the light produced by the transitions described in part (b).

29.

How are the Bohr model and the Rutherford model of the atom similar? How are they different?

30.

The spectra of hydrogen and of calcium are shown here.

What causes the lines in these spectra? Why are the colors of the lines different? Suggest a reason for the observation that the spectrum of calcium is more complicated than the spectrum of hydrogen.

3.3 Development of Quantum Theory

31.

How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?

32.

What are the allowed values for each of the four quantum numbers: n, l, m_l, and m_s?

33.

Describe the properties of an electron associated with each of the following four quantum numbers: n, l, m_l, and m_s.

34.

Answer the following questions:

(a) Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom.

(b) How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?

35.

Identify the subshell in which electrons with the following quantum numbers are found:

(a) n = 2, l = 1

(b) n = 4, l = 2

(c) n = 6, l = 0

36.

Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?

37.

Identify the subshell in which electrons with the following quantum numbers are found:

(a) n = 3, l = 2

(b) n = 1, l = 0

(c) n = 4, l = 3

38.

Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?

39.

Sketch the boundary surface of a $d_{x^{2} − y^{2}}$ and a p_y orbital. Be sure to show and label the axes.

40.

Sketch the p_x and d_xz orbitals. Be sure to show and label the coordinates.

41.

Consider the orbitals shown here in outline.

This figure contains three diagrams. In x, a circle is drawn with a dot at the center. In y, two nearly ellipsoid shapes are oriented horizontally with a dot between them. In z, four shapes like those in y are oriented in an x shape with a dot at the center.

(a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)?

(b) How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?

(c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.

(d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?

(e) What are the possible l and m_l values for an orbital of type (x)? Of type (y)? Of type (z)?

42.

State the Heisenberg uncertainty principle. Describe briefly what the principle implies.

43.

How many electrons could be held in the second shell of an atom if the spin quantum number m_s could have three values instead of just two? (Hint: Consider the Pauli exclusion principle.)

44.

Which of the following equations describe particle-like behavior? Which describe wavelike behavior? Do any involve both types of behavior? Describe the reasons for your choices.

(a) c = λν

(b) $E = \frac{m ν^{2}}{2}$

(c) $r = \frac{n^{2} a_{0}}{Z}$

(d) E = hν

(e) $λ = \frac{h}{m ν}$

45.

Write a set of quantum numbers for each of the electrons with an n of 4 in a Se atom.

3.4 Electronic Structure of Atoms (Electron Configurations)

46.

Read the labels of several commercial products and identify monatomic ions of at least four transition elements contained in the products. Write the complete electron configurations of these cations.

47.

Read the labels of several commercial products and identify monatomic ions of at least six main group elements contained in the products. Write the complete electron configurations of these cations and anions.

48.

Using complete subshell notation (not abbreviations, 1s²2s²2p⁶, and so forth), predict the electron configuration of each of the following atoms:

(a) C

(b) P

(c) V

(d) Sb

(e) Sm

49.

Using complete subshell notation (1s²2s²2p⁶, and so forth), predict the electron configuration of each of the following atoms:

(a) N

(b) Si

(c) Fe

(d) Te

(e) Tb

50.

Is 1s²2s²2p⁶ the symbol for a macroscopic property or a microscopic property of an element? Explain your answer.

51.

What additional information do we need to answer the question “Which ion has the electron configuration 1s²2s²2p⁶3s²3p⁶”?

52.

Draw the orbital diagram for the valence shell of each of the following atoms:

(a) C

(b) P

(c) V

(d) Sb

(e) Ru

53.

Use an orbital diagram to describe the electron configuration of the valence shell of each of the following atoms:

(a) N

(b) Si

(c) Fe

(d) Te

(e) Mo

54.

Using complete subshell notation (1s²2s²2p⁶, and so forth), predict the electron configurations of the following ions.

(a) N^3–

(b) Ca²⁺

(c) S^–

(d) Cs²⁺

(e) Cr²⁺

(f) Gd³⁺

55.

Which atom has the electron configuration 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d²?

56.

Which atom has the electron configuration 1s²2s²2p⁶3s²3p⁶3d⁷4s²?

57.

Which ion with a +1 charge has the electron configuration 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶? Which ion with a –2 charge has this configuration?

58.

Which of the following atoms contains only three valence electrons: Li, B, N, F, Ne?

59.

Which of the following has two unpaired electrons?

(a) Mg

(b) Si

(c) S

(d) Both Mg and S

(e) Both Si and S.

60.

Which atom would be expected to have a half-filled 6p subshell?

61.

Which atom would be expected to have a half-filled 4s subshell?

62.

In one area of Australia, the cattle did not thrive despite the presence of suitable forage. An investigation showed the cause to be the absence of sufficient cobalt in the soil. Cobalt forms cations in two oxidation states, Co²⁺ and Co³⁺. Write the electron structure of the two cations.

63.

Thallium was used as a poison in the Agatha Christie mystery story “The Pale Horse.” Thallium has two possible cationic forms, +1 and +3. The +1 compounds are the more stable. Write the electron structure of the +1 cation of thallium.

64.

Write the electron configurations for the following atoms or ions:

(a) B³⁺

(b) O^–

(c) Cl³⁺

(d) Ca²⁺

(e) Ti

65.

Cobalt–60 and iodine–131 are radioactive isotopes commonly used in nuclear medicine. How many protons, neutrons, and electrons are in atoms of these isotopes? Write the complete electron configuration for each isotope.

66.

Write a set of quantum numbers for each of the electrons with an n of 3 in a Sc atom.

3.5 Periodic Variations in Element Properties

67.

Based on their positions in the periodic table, predict which has the smallest atomic radius: Mg, Sr, Si, Cl, I.

68.

Based on their positions in the periodic table, predict which has the largest atomic radius: Li, Rb, N, F, I.

69.

Based on their positions in the periodic table, predict which has the largest first ionization energy: Mg, Ba, B, O, Te.

70.

Based on their positions in the periodic table, predict which has the smallest first ionization energy: Li, Cs, N, F, I.

71.

Based on their positions in the periodic table, rank the following atoms in order of increasing first ionization energy: F, Li, N, Rb

72.

Based on their positions in the periodic table, rank the following atoms in order of increasing first ionization energy: Mg, O, S, Si

73.

Atoms of which group in the periodic table have a valence shell electron configuration of ns²np³?

74.

Atoms of which group in the periodic table have a valence shell electron configuration of ns²?

75.

Based on their positions in the periodic table, list the following atoms in order of increasing radius: Mg, Ca, Rb, Cs.

76.

Based on their positions in the periodic table, list the following atoms in order of increasing radius: Sr, Ca, Si, Cl.

77.

Based on their positions in the periodic table, list the following ions in order of increasing radius: K⁺, Ca²⁺, Al³⁺, Si⁴⁺.

78.

List the following ions in order of increasing radius: Li⁺, Mg²⁺, Br^–, Te^2–.

79.

Which atom and/or ion is (are) isoelectronic with Br⁺: Se²⁺, Se, As^–, Kr, Ga³⁺, Cl^–?

80.

Which of the following atoms and ions is (are) isoelectronic with S²⁺: Si⁴⁺, Cl³⁺, Ar, As³⁺, Si, Al³⁺?

81.

Compare both the numbers of protons and electrons present in each to rank the following ions in order of increasing radius: As^3–, Br^–, K⁺, Mg²⁺.

82.

Of the five elements Al, Cl, I, Na, Rb, which has the most exothermic reaction? (E represents an atom.) What name is given to the energy for the reaction? Hint: Note the process depicted does not correspond to electron affinity.)
$E^{+} (g) + e^{−} ⟶ E (g)$

83.

Of the five elements Sn, Si, Sb, O, Te, which has the most endothermic reaction? (E represents an atom.) What name is given to the energy for the reaction?
$E (g) ⟶ E^{+} (g) + e^{-}$

84.

The ionic radii of the ions S^2–, Cl^–, and K⁺ are 184, 181, 138 pm respectively. Explain why these ions have different sizes even though they contain the same number of electrons.

85.

Which main group atom would be expected to have the lowest second ionization energy?

86.

Explain why Al is a member of group 13 rather than group 3?

3.6 The Periodic Table

87.

Using the periodic table, classify each of the following elements as a metal or a nonmetal, and then further classify each as a main-group (representative) element, transition metal, or inner transition metal:

(a) uranium

(b) bromine

(c) strontium

(d) neon

(e) gold

(f) americium

(g) rhodium

(h) sulfur

(i) carbon

(j) potassium

88.

Using the periodic table, classify each of the following elements as a metal or a nonmetal, and then further classify each as a main-group (representative) element, transition metal, or inner transition metal:

(a) cobalt

(b) europium

(c) iodine

(d) indium

(e) lithium

(f) oxygen

(g) cadmium

(h) terbium

(i) rhenium

89.

Using the periodic table, identify the lightest member of each of the following groups:

(a) noble gases

(b) alkaline earth metals

(c) alkali metals

(d) chalcogens

90.

Using the periodic table, identify the heaviest member of each of the following groups:

(a) alkali metals

(b) chalcogens

(c) noble gases

(d) alkaline earth metals

91.

Use the periodic table to give the name and symbol for each of the following elements:

(a) the noble gas in the same period as germanium

(b) the alkaline earth metal in the same period as selenium

(c) the halogen in the same period as lithium

(d) the chalcogen in the same period as cadmium

92.

Use the periodic table to give the name and symbol for each of the following elements:

(a) the halogen in the same period as the alkali metal with 11 protons

(b) the alkaline earth metal in the same period with the neutral noble gas with 18 electrons

(c) the noble gas in the same row as an isotope with 30 neutrons and 25 protons

(d) the noble gas in the same period as gold

93.

Write a symbol for each of the following neutral isotopes. Include the atomic number and mass number for each.

(a) the alkali metal with 11 protons and a mass number of 23

(b) the noble gas element with 75 neutrons in its nucleus and 54 electrons in the neutral atom

(c) the isotope with 33 protons and 40 neutrons in its nucleus

(d) the alkaline earth metal with 88 electrons and 138 neutrons

94.

Write a symbol for each of the following neutral isotopes. Include the atomic number and mass number for each.

(a) the chalcogen with a mass number of 125

(b) the halogen whose longest-lived isotope is radioactive

(c) the noble gas, used in lighting, with 10 electrons and 10 neutrons

(d) the lightest alkali metal with three neutrons

3.7 Molecular and Ionic Compounds

95.

Using the periodic table, predict whether the following chlorides are ionic or covalent: KCl, NCl₃, ICl, MgCl₂, PCl₅, and CCl₄.

96.

Using the periodic table, predict whether the following chlorides are ionic or covalent: SiCl₄, PCl₃, CaCl₂, CsCl, CuCl₂, and CrCl₃.

97.

For each of the following compounds, state whether it is ionic or covalent. If it is ionic, write the symbols for the ions involved:

(a) NF₃

(b) BaO,

(c) (NH₄)₂CO₃

(d) Sr(H₂PO₄)₂

(e) IBr

(f) Na₂O

98.

For each of the following compounds, state whether it is ionic or covalent, and if it is ionic, write the symbols for the ions involved:

(a) KClO₄

(b) Mg(C₂H₃O₂)₂

(c) H₂S

(d) Ag₂S

(e) N₂Cl₄

(f) Co(NO₃)₂

99.

For each of the following pairs of ions, write the symbol for the formula of the compound they will form.

(a) Ca²⁺, S²⁻

(b) ${NH}_{4}^{+},$ ${SO}_{4}^{2−}$

(c) Al³⁺, Br⁻

(d) Na⁺, ${HPO}_{4}^{2−}$

(e) Mg²⁺, ${PO}_{4}^{3−}$

100.

For each of the following pairs of ions, write the symbol for the formula of the compound they will form.

(a) K⁺, O²⁻

(b) ${NH}_{4}^{+},$ ${PO}_{4}^{3−}$

(c) Al³⁺, O²⁻

(d) Na⁺, ${CO}_{3}^{2−}$

(e) Ba²⁺, ${PO}_{4}^{3−}$

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Key Equations

Summaries

3.1Electromagnetic Energy

3.2The Bohr Model

3.3Development of Quantum Theory

3.4Electronic Structure of Atoms (Electron Configurations)

3.5Periodic Variations in Element Properties

3.6The Periodic Table

3.7Molecular and Ionic Compounds

Exercises

3.1 Electromagnetic Energy

3.2 The Bohr Model

3.3 Development of Quantum Theory

3.4 Electronic Structure of Atoms (Electron Configurations)

3.5 Periodic Variations in Element Properties

3.6 The Periodic Table

3.7 Molecular and Ionic Compounds

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